Stats Lecture Notes 2.docx

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Ramesh Balasubramaniam

Stats Lecture 5 Fall Non-Parametric Data “ Parametric Tests” – look at one parameter and how its correlated to other variables - Estimation of population parameters from sample parameters - Must satisfy several assumptions: independence, normality, homogeneity Independence - Participants are randomly assigned to treatment conditions - Only one observation per participant Normality - Data (scores) are distributed normally - Not skewed or bimodal - Can fix and make a curve normal or put it into another distribution.. - Cannot use parametric tests anymore once perfect normality is violated Homogeneity - Variances across groups and/or treatment conditions are “reasonably” similar - Often a problem in Special Populations research where one group (and the scores they generate) may be fundamentally different from another group Analysis of Non-Parametric Data “Parametric” - Normal distribution - Interval or ratio data - Often data do not fit these criteria… nominal, ordinal (ranked) - Exercise physiology  questionnaire data, rank orderings, inter-rater reliabilities, etc - Hypothesis testing and associative analyses can be used on these data; most common are: o Chi square, spearman rank order correlation, mann-whitney U test, kruskal-wallace ANOVA by Ranks 2 Chi Square (x ) - Compares two or more sets of Nominal data that have been arranged by frequency counts - There is no variability within a category o Categories are mutually exclusive o All observations are of equal value - Provides information as to whether a relationship between two independent variables occur by chance alone - Computed from tables of frequencies o Comparison of counts o Assesses discrepancies between:  Expected frequency (chance)  Observed frequency - Letter grades are a good example; there will be a frequency distribution of A, B, C, D,… etc. o These are nominal data IF all we are concerned with is the frequency of occurance o A=B=C=D 2 o X analysis will determine If the frequencies within each category differ by amounts larger than chance - H 0ssumes any differences occurred by chance - If H0is not true, some other factor must be involved to influence the changes in the frequency count - Chance principle: “is what has been observed the same or different from what is expected?” - - Sum of the squared differences between observed and expected scoeres after dividing b the expected frequency - Example: - Does gender influence adherence to a cardiac rehab program? - IV1 = Gender (make, female) , 1V2 = adherence (stayed in, dropped out) - Computing a 2x2 Chi square: - This is called a Tabular analysis (aka crossbreaks) .. usually these tables are bivariate - Summarizes the “intersection” of IVs and DVs IV(1) 1 2 IV(2) 1 DV DV 2 DV DV - Tabl
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